In the air transport industry, research studies have been conducted for many years to reduce the vibrations and noise produced by the engines. Various techniques have been used.
Passive or active balancing techniques are also known, in which the inertial or aerodynamic imbalance is measured and corrected, as is the case for example in document WO-2006/017201.
Other “synchrophasing” techniques are also known, where synchrophasing between several engines limits the noise generated at the blade passing frequency, as is the case for example in documents U.S. Pat. No. 4,689,821, US-2005/0065712, WO-2005/042959 and US-00/5221185. The main problem with these techniques for balancing and synchrophasing by the engine control system is that the control system delay must be much less than the period separating the passage of two blades in front of the sensor used. This is never the case, however, which means that no industrial applications can be considered.
Techniques to filter and attenuate the vibrations generated in the aircraft are also known. They consist for example of active or semi-active systems with active weights, variable stiffness or rheological fluids (as described in document U.S. Pat. No. 5,490,436). These techniques also include systems equipped with sensors and control architectures to command active or semi-active actions. These techniques have been developed to limit the impact of imbalance forces on the supporting structure.
In reference to FIG. 1, we will first describe the imbalance problem for a single rotating disc. This figure shows a disc forming a propeller 2 comprising blades 4, in this case eight. The propeller can rotate freely around an axis 6 corresponding to its main geometric axis of symmetry. We assume that the propeller has a balancing fault such that the center of gravity of the propeller is not on axis 6 but is shifted radially from it. This center of gravity 8 is for example located on one of the blades 4, as shown, rather exaggerated, on FIG. 1. We assume that the propeller is rotated around its axis 6 in the direction shown by the arrow 10. The center of gravity 8 therefore generates an imbalance force 12 exerted on the propeller on the axis 6 in the plane of the disc along a radial direction towards the outside and passing through point 8. This force rotates in direction 10. It is an inertial imbalance. Consequently, for any rotating disc whose center of inertia does not coincide with the center of rotation, an inertial imbalance produces a radial force in the plane of the disc as shown on FIG. 1.
In reference to FIG. 2, there may also be an aerodynamic imbalance. This is the case when the moving disc comprises bearing surfaces such as the faces of propeller blades. A setting fault or a shape fault on the bearing surfaces may therefore generate an aerodynamic imbalance. There could also be a problem of dispersion of aerodynamic deformation of the blades or of dispersion of the blade pitch. The aerodynamic imbalance force is exerted at a point 14 located away from axis 6. The imbalance force is composed firstly of a traction force increment referenced 16 on FIG. 2 and located outside the plane of the propeller disc, and a drag force increment 18 located in the plane of the propeller disc.
We will now describe some balancing techniques in greater detail. We know in fact how to measure the imbalance forces of a rotating machine (or of a rotating disc), distinguishing between the amplitude and the phase angle of the force with respect to a fixed axis. One of these techniques is as follows for example. To eliminate the vibrations at a specific speed of rotation, we first measure the imbalance characteristics of the rotating machine. We therefore measure or calculate the imbalance forces it produces. These forces are characterized by a sinusoidal excitation in the engine speed frequency range in a fixed reference coordinate system with respect to the rotating part, for example related to the supporting structure. These excitations are generally measured using an engine vibration sensor (e.g. an accelerometer) or a set of dedicated accelerometers. The imbalance of a rotating disc is therefore represented by the measured acceleration R1 in terms of amplitude (gain) and phase (φ) in the axis of the fixed supporting structure at the machine speed of rotation ωo as shown on FIG. 3. This figure shows on a first curve 20 the graph of gain (in m/s−2) against speed of rotation ω (in rad/s), and on the second curve 22 the graph of phase φ (in radians) against this speed.
The following measurement method, called the vector influence coefficient method, can be used. After measuring the initial acceleration R1, which represents the result of the action of the imbalance required, imbalance masses of known weight are added to the rotating system to measure their effect on the measured acceleration. For example, an imbalance of unit mass is added to the disc at phase angle 0° and a new acceleration R2 (gain and phase) at speed ωo is measured.
We then calculate a vector solution as follows:                the original imbalance b1 causes acceleration R1,                    the set (b1+b2) forming the sum of the original imbalance and of the unit imbalance causes an acceleration R2,                        by deduction, the unit imbalance b2 therefore generates the acceleration R2−R1. Concerning this subject, we refer to FIG. 4 which shows in an orthonormal coordinate system the vectors R1, R2 and R2−R1 which have respectively phases φR1, φR2 and φ(R2−R1).        
Note here that this calculation method assumes that there is a linear relation between the imbalance and the corresponding measured acceleration.
The original imbalance and the correction mass required as a result are therefore calculated as follows:
         {                                                                                                      b                  1                                →                                                    =                                                                                                b                    2                                    →                                                            ·                                                                                                            R                      1                                        →                                                                                                                                                                          R                        2                                            →                                        -                                                                  R                        1                                            →                                                                                                                                                                            φ                                                b                  _                                1                                      =                                          φ                                                      b                    _                                    2                                            +                              φ                                                      R                    _                                    1                                            -                              φ                                                                            R                      _                                        2                                    -                                                            R                      _                                        1                                                                                          
To obtain better results and minimize the measurement errors, several steps of adding weights and measuring accelerations, with accelerations R3 and R4 for example, can be carried out.
Note that the inertial and aerodynamic imbalances may have to be measured separately. The above-mentioned technique can be used to do this, providing in addition that modifications of the speed of rotation and independent modifications of the torque request can be made, in order to distinguish between the source of imbalance due to inertia and the source of imbalance due to the aerodynamic characteristics of the rotor.
Similarly, when the rotating machine comprises two or, more rotors, the same approach can be reproduced for each rotor disc one after the other. In this case, imbalance diagnostic software programs supply balancing solution vectors which include one solution vector for the first rotor and one solution vector for the second rotor. Each solution vector includes a modulus and a phase angle. This operation will be carried out to characterize the inertial imbalance and then to characterize the aerodynamic imbalance.
We will now describe, in reference to FIG. 5, the problem of imbalance of two counter-rotating discs. As for a single disc, with two counter-rotating discs, the inertial imbalance of each disc produces a radial force in the plane of the corresponding disc. FIG. 5 shows these forces PROP1 24 and PROP2 26 which are exerted at the axis of rotation 6 common to the two discs. The two discs rotate in different directions, indicated respectively 28 and 30 on FIG. 5. The imbalance forces 24 and 26 also rotate in opposite directions, respectively 28 and 30.
We now consider the force PROP 1+2 resulting from the sum of the two imbalance forces PROP1 and PROP2 as observed from the sump of the rotating machine or its supporting structure. The modulus of this resultant force varies depending on the relative position of the discs. Over time, this modulus describes an ellipse 32 centered on the axis 6, whose minor axis is equal to the difference between the moduli of forces PROP1 and PROP2 and a major axis 34 equal to the sum of the two moduli.
We now consider the special case wherein the moduli of the two forces PROP1 and PROP2 are equal. Consequently, the length of the minor axis of the ellipse is zero and the resultant force PROP 1+2 is equal to the sum of the moduli of the two forces, making it a pure oscillating impact force. The ellipse is therefore reduced to a line segment. For example, if we assume that phase φ is equal to 0 when the two radial forces PROP1 (or Rdisc1) and PROP2 (or Rdisc2) are in phase, the resultant radial force R can be described as follows:R(ωt)=Rdisc1(ωt)+Rdisc2(ωt)R(ωt+π/2)=Rdisc1(ωt+π/2)−Rdisc2(ωt+π/2)R(ωt+π)=−[Rdisc1(ωt)+Rdisc2(ωt)]R(ωt+3π/2)=Rdisc2(ωt+3π/2)−Rdisc1(ωt+3π/2)
In addition, the resultant moment M outside the plane can be described as follows:M(ωt)=0M(ωt+π/2)=[Rdisc1(ωt)+Rdisc2(ωt)]*leverarmM(ωt+π)=0M(ωt+3π/2)=−[Rdisc1(ωt)+Rdisc2(ωt)]*leverarm
The moment located outside the plane is expressed at the center of the disc 1 for example. In addition, the lever arm is the axial distance between the planes of discs 1 and 2.
The direction of the major axis of the ellipse depends on the relative phase between the imbalance forces PROP1 and PROP2. For example, if the positions of the two discs are such that the two forces are in phase in the vertical axis, the maximum excitation in the plane of the discs will be directed vertically. In contrast, if the positions of the two discs are such that the two forces are in phase opposition (180° shift) in the vertical direction, the maximum excitation in the plane of the discs will be directed horizontally.
When the two counter-rotating discs incorporate aerodynamic bearing surfaces, the forces located outside the planes of the discs generate moments passing through the center of rotation of each disc. Consequently, as with the case of the inertial imbalance, the principle of vector summing described for the radial forces is applicable for the moments generated by the aerodynamic imbalance forces as shown on FIG. 6. This figure shows Moment 1 referenced 38 associated with disc 1 rotating in direction 28 and Moment 2 referenced 40 associated with disc 2 and rotating in direction 42. The vector sum Moments 1+2 of the two moments describes an ellipse 44.
Whether in case of inertial imbalance or aerodynamic imbalance, when the two discs rotate at the same speed, the major axis of the ellipse remains fixed with respect to a fixed axis corresponding for example to the engine supporting structure. Inversely, if the speeds of rotation of the discs are not the same, the axis of the ellipse rotates at a speed equal to the difference between the speeds of the two discs.
Note here that in addition to the rotating forces located outside the plane of the discs, local moments are generated between the two planes of the discs. The moduli of these moments depend on the distance between the two rotating discs.
The known vibration reduction techniques prove relatively inefficient, however, especially for engines having counter-rotating rotors.